In a statement following their meeting, the quartet said that both Israel and the Palestinians need "to refrain from unilateral actions that make a two-state solution more difficult to achieve."
It appeared to be the first time since September 2018 that envoys from the four mediators have met. Last month, U.N. Secretary-General Antonio Guterres said he hoped there would be a quartet meeting in coming weeks, now that there was a new president in the White House.
The Palestinians want a state in the West Bank and Gaza Strip with east Jerusalem as its capital - all territory captured by Israel in 1967. Under a failed peace proposal by former U.S. President Donald Trump, Washington would have recognized Jewish settlements in occupied territory as part of Israel.
The new administration of President Joe Biden has said it supports a two-state solution between Israel and the Palestinians and will overturn several decisions made by Trump.
It has said it will continue to urge other countries to normalize ties with Israel, but stressed that is not a substitute for Israeli-Palestinian peace.In what is widely seen as one of Trump's few foreign policy successes, Washington secured agreements late last year by four Arab states - the United Arab Emirates, Bahrain, Sudan and Morocco - to start normalizing relations with Israel.