The meeting, which had been put off by a day, began in the late afternoon in a Jerusalem hotel, Palestinian sources said.
The discussions are "very difficult", one source said.
Israel implied that the delay had been caused by the killing of an Israeli police officer in the West Bank this week, but the Palestinians said the meeting was pushed from yesterday to today to enable Indyk to take part.
State Department spokeswoman Jennifer Psaki said this week that Israeli and Palestinian negotiators are striving to reach an agreement to extend the talks beyond their April 29 deadline.
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Washington is pushing for an extension but the negotiations hit an impasse two weeks ago when Israel refused to release a group of Palestinian prisoners as agreed at last year's launch of the talks.
Among them are 14 Arab Israelis which the Jewish state is refusing to set free.
The Palestinians retaliated by seeking accession to several international treaties.
Today's new round of talks came as Palestinians marked Prisoners Day with rallies across the West Bank and Gaza Strip in solidarity with thousands of their jailed compatriots.
Chief Palestinian negotiator Saeb Erakat added his voiced to the protesters on today by calling anew on Israel to free the last batch of prisoners.
Despite the crisis, Palestinian president Mahmud Abbas's spokesman Nabil Abu Rudeina stressed the talks could be extended if Israel released the last batch of prisoners.
"What's needed now is Israel's commitment on issues that could lead to an extension of talks. If they commit, we're ready," he said on yesterday.