Netanyahu, whose right-leaning government took office on March 31, said he "intended to resume" talks and co-operation with the Palestinians for the sake of promoting peace, the statement said.
Abbas has said that Israel's new government must commit to a two-state solution before the resumption of peace talks.
Until now, the only comments on the peace process to come from the new Israeli administration had come from Avigdor Lieberman, the Israeli foreign minister, who said the new cabinet was not bound by a 2007 US-backed agreement to revive negotiations.
Analysts have expressed concern that Netanyahu's hawkish government could mean a further stalling of the peace process.
Yisrael Katz, the Israeli transport minister, who is close to Netanyahu, said on Sunday that Hassan Nasrallah, the head of Lebanon's Shia Hezbollah movement, should be killed.
"Nasrallah deserves death and I hope that those who know what to do with him will act and give him what he deserves," Katz said.
His remarks came after Cairo announced last week the arrest of 49 people linked with Hezbollah on suspicion of planning attacks in Egypt.
Nasrallah confirmed on Friday that one of those detained is a Hezbollah member, but denied seeking to destabilise Egypt, saying the man was responsible for helping transport arms to Hamas, the Palestinian group that controls the Gaza Strip.