Mr Khashoggi, a Saudi national, went missing after visiting the Saudi consulate in Istanbul on Tuesday.
A Turkish official told the BBC that initial investigations indicated he was murdered there.
Saudi Arabia has denied the accusations, saying it is "working to search for him".
The Washington Post said it would be a "monstrous and unfathomable act" if he had been killed.
The BBC's Istanbul correspondent, Mark Lowen, said it would plunge Turkish-Saudi relations into an unprecedented crisis.
Turkish officials have opened an investigation and have been speaking to the media on condition of anonymity.
The deputy chairman of Turkey's ruling AK Party told broadcaster CNN Turk there was concrete evidence, according to Reuters news agency, but none has yet been presented.
When was he last seen?
Jamal Khashoggi is a high-profile critic of Saudi Arabia's Crown Prince Mohammed bin Salman. He has more than 1.6 million Twitter followers and has written for the Washington Post opinion section.
On Tuesday, he went to the consulate to obtain a document certifying he had divorced his ex-wife, so that he could marry his Turkish fiancée, Hatice Cengiz.
Ms Cengiz said she waited outside for 11 hours, but he did not come out.
She said Mr Khashoggi was required to surrender his mobile phone, which is standard practice in some diplomatic missions. He told her to call an adviser to Turkish President Recep Tayyip Erdogan if he did not return.

Jamal Khashoggi's fiancée Hatice waited outside the Saudi consulate on Wednesday EPA
"Jamal is not dead. I cannot believe that he has been killed...!" Ms Cengiz wrote on Twitter as the allegations circulated. She said she was waiting for official confirmation.
The head of the Turkish-Arab Media Association, Turan Kislakci, told the New York Times that Turkish police officers providing security for the consulate had checked their security cameras and did not see the journalist leave on foot. But he added that diplomatic cars had been seen moving in and out.
What have the Saudis said?
On Wednesday, Crown Prince Mohammed bin Salman told Bloomberg News that Turkish authorities were welcome to search the building because "we have nothing to hide".
The prince said the Saudis were "very keen to know what happened to him", saying his understanding was that Mr Khashoggi left "after a few minutes or one hour".

The Saudi consulate said Khashoggi left after completing paperwork AFP
When asked if Mr Khashoggi faced charges in Saudi Arabia, the crown prince said his country would need to know where he was first.
Potential crisis
Analysis by the BBC's Mark Lowen, Istanbul
This is a bombshell allegation by Turkey. And while the authorities here are so far not providing evidence to back it up, it's inconceivable that such a claim would have been made without firm grounds. Ankara's relationship with Riyadh is too important to jeopardise on the basis of unsubstantiated rumour.
That relationship is already strained over several issues, including Turkey's support for Qatar in the blockade by Saudi Arabia; its closeness to the Muslim Brotherhood - blacklisted by Riyadh as a terrorist organisation; and its rapprochement with Saudi Arabia's arch-rival Iran. But if proven, the murder of Jamal Khashoggi would be the most serious diplomatic crisis between the two in living memory.
Turkey would hope for backing from its Nato ally, the US. But Saudi Arabia has arguably become Donald Trump's closest ally in the Middle East - and Washington may be reluctant to weigh in against Riyadh at this stage.
Who is Jamal Khashoggi?
The 59-year-old journalist is one of the most prominent critics of the crown prince, who has unveiled reforms praised by the West while carrying out an apparent crackdown on dissent. Human and women's rights activists, intellectuals and clerics have been arrested - meanwhile, Saudi Arabia is waging a war in Yemen that has triggered a humanitarian crisis.
A former editor of the al-Watan newspaper and a short-lived Saudi TV news channel, Mr Khashoggi was for years seen as close to the Saudi royal family. He served as an adviser to senior Saudi officials.
After several of his friends were arrested, his column was cancelled by the al-Hayat newspaper and he was allegedly warned to stop tweeting, Mr Khashoggi left Saudi Arabia for the US, from where he wrote opinion pieces for the Washington Post and continued to appear on Arab and Western TV channels.
"I have left my home, my family and my job, and I am raising my voice," he wrote in September 2017. "To do otherwise would betray those who languish in prison. I can speak when so many cannot."
The Washington Post on Friday blanked out his column in support.
Courtesy: www.bbc.com
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Bengaluru (PTI): After 44 peacocks died of the H5N1 virus in Tumakuru district, Karnataka Minister Eshwar Khandre on Saturday directed officials to implement strict precautionary measures to prevent its spread across forest areas, including zoos and bird sanctuaries.
The directive comes after laboratory reports from the ICAR–National Institute of High Security Animal Diseases in Bhopal recently confirmed H5N1 avian influenza as the cause of the deaths.
According to the state forest minister, the peacocks died between April 16 and 21 in and around Bommanahalli and Kolihalli villages in Urdigere hobli, and Bairasandra and Hullenahalli villages in Gulur hobli of Tumakuru district.
“In this context, instructions have been issued in line with the revised H5N1 Action Plan of the Central Government to prevent the spread of infection across all forest areas, including zoos, bird sanctuaries, Magadi Lake, and the community reserve at Kokkare Bellur,” Khandre said in a note addressed to the principal chief conservator of forests (wildlife) and chief wildlife warden.
He also directed that any deaths of birds, whether migratory or local, must be reported immediately, and that samples from carcasses should be collected and sent for testing.
If required, a nodal officer may be appointed to monitor the situation across the state, he added.
Authorities have established an infected zone within a 0–3 km radius and a surveillance zone extending from 3 to 10 km.
According to the Health Department, surveillance for fever, Influenza-Like Illness (ILI), and Severe Acute Respiratory Infection (SARI) will be carried out over the next 10 days, covering a population of 20,432 across 38 villages.
In light of the situation, the department has advised the public to follow precautionary measures to minimise the risk of infection by avoiding contact with sick or dead birds and maintaining hand hygiene by washing hands frequently with soap and water.
It has also suggested the use of personal protective equipment (PPE) while handling birds or their droppings, and advised ensuring that poultry and eggs are thoroughly cooked (above 80 degrees celcius) before consumption.
The health department has also recommended avoiding close contact with individuals exhibiting symptoms of respiratory illness.
The department said it is closely monitoring the situation and has put necessary precautionary measures in place.
The public has been advised to remain vigilant and report any unusual bird deaths or symptoms promptly, officials added.
Avian influenza (H5N1) is a subtype of the influenza virus that infects birds and mammals, including humans in rare instances, according to the World Health Organisation. Human cases reported so far have been mostly linked to close contact with infected birds or other animals, or with contaminated environments.
