Israel and the Palestinians held a second negotiating session at a secret location in Jerusalem on Tuesday, Israel Radio reported, quoting a member of the Palestinian team, dpa reported.
News that the session was taking place was not officially made public, because the participants have agreed to continue the talks outside the media spotlight.
A first session in Jerusalem last week marked the end of a three-year absence of direct negotiations.
US envoy Martin Indyk had met Palestinian President Mahmoud Abbas late on Monday, urging him to continue the talks, despite ongoing Israeli construction in the West Bank and East Jerusalem, the radio added.
Israel's chief negotiator, Tzipi Livni, told Israel Radio on Tuesday that Prime Minister Benjamin Netanyahu's centre-right coalition was impeding the negotiations.
"It's no secret that there is a party in the coalition" which opposes negotiations and a two-state solution of the Israeli-Palestinian conflict, Livni said.
This was a reference to the ultra-nationalist, pro-settler Jewish Home party, which has 12 seats in the 120-seat Israeli parliament.
Livni, a centrist, is a supporter of the two-state solution and is seen as a dovish member of Netanyahu's coalition.
Follow us on Twitter @TRENDNewsAgency