News reports and Turkish investigators have pointed culpability squarely at a crew of Saudis who reportedly interrogated, killed and even dismembered the Saudi journalist. Saudi officials deny any involvement in his disappearance.
Pompeo stressed that the USA and Saudi Arabia have important links, including working on countering Iran.
The decision marks a turnaround for Ms Lagarde, who had previously said she was "horrified" by reports coming out of Turkey but would still attend the Saudi conference. "If they knew about it, that would be bad", he said during an interview on Tuesday.
A possible conflict with the Saudis would also send oil prices skyrocketing, something that the White House doesn't want, the analyst added.
By casting doubt on whether the United States will respond at all, Pompeo reflected the internal struggle among Trump and his national security advisers on what to do should the Saudi leadership be blamed for what happened to Khashoggi.
Khashoggi, a critic of Saudi policy who has written for The Washington Post and other publications, has not been seen since he entered the Saudi Consulate in Istanbul two weeks ago.More news: Djokovic cruises past Coric to win fourth Shanghai title
After investigations at the Saudi consulate and the consul's residence, Turkish authorities have widened the geographic focus of the search, the senior Turkish officials said.
The Crown Prince told Pompeo that the USA and Saudi Arabia "are strong and old allies".
It said al-Otaibi can be heard on one tape saying during Khashoggi's torture: "Do this outside".
The Netherlands said Finance Minister Wopke Hoekstra was no longer going to the conference, and that it was also canceling a planned trade mission to Saudi in December.
The statement continued: "We encourage Turkish-Saudi collaboration and look forward to the Kingdom of Saudi Arabia conducting a thorough, credible, transparent, and prompt investigation, as announced".
A Turkish paper has alleged that an "assassination squad" of 15 Saudi men flew into Istanbul on October 2, hours before Khashoggi was last seen entering the Saudi consulate.
Asked why the USA seemed to give Saudi Arabia the benefit of the doubt, given the preponderance of signs that there was high-level Saudi involvement, Pompeo said "it is reasonable to give them a handful of days more to complete it, so they get it right, so that it's thorough and complete".