JERUSALEM, Jan 30 (Reuters) - Prime Minister Benjamin Netanyahu said on Sunday Israel must exercise responsibility and restraint in the face of unrest in Egypt and hoped that stability and peaceful ties with Cairo would last.

Protests against Egyptian President Hosni Mubarak's rule have worried Israel, which signed a peace treaty with its largest Arab ally more than 30 years ago, and uncertainty over Egypt's future has raised fears about stability in the region.

We are following with vigilance the events in Egypt and in our region ... at this time we must show responsibility and restraint and maximum consideration, Netanyahu told his cabinet, in his first public response since the protests began.

Netanyahu said he had spoken to US President Barack Obama, Secretary of State Hillary Clinton and to decision-makers in Israel. He urged ministers to refrain from further comment.

Our efforts have been intended to continue to preserve stability and security in our region, Netanyahu added, addressing cabinet ministers in public remarks.

I remind you that the peace between Israel and Egypt has lasted for over three decades. He said he sought to ensure that these relations will continue to exist.

Egypt was the first Arab country to sign a treaty with Israel, in 1979. Jordan followed suit in 1994. (Writing by Allyn Fisher-Ilan and Ori Lewis; Editing by Andrew Dobbie)