Sheikh Hamad bin Jassem bin Jabr al-Thani arrived in Gaza City late on Monday and went straight into talks with Mahmoud Abbas, the Palestinian president.
He later met Ismail Haniya, the Palestinian prime minister from the Hamas.
"He will discuss the forming of a national unity government and will try to bring both sides closer," one official said on condition of anonymity.
Nabil Abu Rudeina, a Palestinian presidential spokesman, had earlier confirmed that Abbas would meet Sheikh Hamad "in order to continue discussion which started last week" when Abbas visited the Qatari capital Doha.
Qatar has put forward proposals to Khaled Meshaal, the Hamas leader, designed to end a standoff that has prevented the formation of a new Palestinian government and triggered the worst internal violence in a decade.
The present Hamas-led Palestinian government has been embroiled in a bitter power struggle with President Abbas of the once-dominant Fatah faction that has raised fears of civil war.
"There is a Qatari initiative on the table to narrow Palestinian differences. We cannot discuss the details, but Hamas is committed to a national unity government"
Izzat Mohammad Rishq, a Hamas member
Palestinian politicians said the proposals included forming a "technocratic government" and a meeting between Abbas and Meshaal, whose Hamas movement won Palestinian elections in January. Some Hamas leaders like Meshaal live in exile.
Izzat Mohammad Rishq, a high-level Hamas member, told Reuters: "There is a Qatari initiative on the table to narrow Palestinian differences. We cannot discuss the details, but Hamas is committed to a national unity government".
The key obstacles to the formation of a government have been Hamas' refusal to participate in any administration that recognises Israel and to renounce armed struggle against the Jewish state.
"The Qataris are trying to find a way around this. Hamas thinks that Abbas is also under pressure and views his latest moves as an attempted coup," said one Palestinian politician, asking not to be named.
Qatar's foreign minister is attempting to negotiate a deal between Abbas and Haniya.
"He will discuss the forming of a national unity government and will try to bring both sides closer," a senior official said.
Hamas agreed to a national unity deal in September based on a reconcilation document drawn up by Palestinian prisoners in Israel, but talks have stalled over the movement's refusal to recognise Israel.
Abbas last week gave Hamas another two weeks to accept a political programme which would be acceptable to the US and the UN, saying that talks had broken down completely.
The talks have since been overshadowed by violent clashes between Hamas loyalists and supporters of Abbas's Fatah movement.
Abbas's Fatah movement argues the president has the right to call early parliamentary elections, but Hamas disputes this.