"We welcome the meetings in Amman… which led to an improvement in the situation, especially around the mosques compound," he said, quoted by the Palestinian news agency WAFA.
On Friday, Israel lifted restrictions on Muslims praying at Jerusalem's flashpoint Al-Aqsa mosque, a day after US Secretary of State John Kerry held talks in the Jordanian capital and announced an agreement on steps to reduce tensions.
The mosque compound, holy to Jews and Muslims, has been the focus of months of unrest in east Jerusalem.
Palestinians have been infuriated by a far-right Jewish campaign for prayer rights at Al-Aqsa that threatens an ultra-sensitive, decades-old status quo that allows only Muslims to pray there.
The violence prompted Kerry to meet the two sides in neighbouring Jordan on Thursday, after which he announced that confidence-building measures had been agreed.
Steinmeier, who held talks in the West Bank town of Ramallah with Palestinian leader Mahmud Abbas and is to meet Israeli leaders on Sunday, said a return to the negotiating table was the only way forward.
"At present, there is no room or the necessary conditions for a resumption of negotiations, and the main thing for now is to ease tensions," he said.
But "there is no alternative to negotiations to reach a two-state solution… a Palestinian state living in peace and security alongside Israel."
Steinmeier's visit came as the Palestinians marked the 26th anniversary of a symbolic declaration of independence by the Palestine Liberation Organisation's parliament, which at the time met in exile in Algiers.