Palestinian Authority President Mahmoud Abbas has given Hamas until the end of the week to accept a plan for statehood that implicitly recognises Israel.
Tensions between Hamas and Fatah have worsened recently
Mr Abbas's plan to hold a referendum on his two-state plan has been approved by the PLO's executive committee.
But Hamas Prime Minister Ismail Haniya said more talks were needed and urged Mr Abbas not to use "the language of days and time as a threat".
Hamas, which heads the government, has said a referendum would be illegal.
But the poll was endorsed by the PLO - the umbrella organisation that represents Palestinians in and outside the occupied territories.
PLO executive member, Yasser Abed Rabbo, said the referendum was aimed at achieving a national consensus.
"We want to achieve the results. We want to have national consensus. This is our target and our aim," Mr Rabbo said.
In other developments on Tuesday:
- Three people are hurt in an explosion at Mr Abbas's security headquarters in the Gaza Strip
- Palestinian militants fire rockets at the southern Israeli town of Sderot, injuring one woman
Hamas does not recognise Israel and has so far rejected Mr Abbas's plans for a Palestinian state taking shape alongside the Jewish state.
A Hamas official, parliamentary speaker Aziz Dueik, said his party opposed Mr Abbas's call for a referendum while "there is hunger and famine because of the international boycott of the Palestinians".
But he said Hamas had not rejected the referendum because it was opposed to a two-state solution.
"Everybody in Hamas says 'Yes' to the two-state solution," he said.
"The problem comes from the fact that the Israelis so far did not say - we do accept the 1967 borders as the international accepted... borders between the two states."
Hamas is insisting that talks must continue without the threat of an ultimatum.
"We still have a chance to make this dialogue a success," Mr Haniya said. "Therefore we ask for more meetings and more dialogue and that we don't use the language of days and time as a threat."
"We cannot accept that the dialogue has failed. We cannot decide this after just one or two additional meetings as there are many strategic questions to be addressed," he added.
On 25 May, Mr Abbas said he gave factions 10 days to accept his statehood plan or else he would call a referendum on the issue.
Talks held on Monday broke down one hour before the deadline expired.
Tension between Fatah and Hamas has been growing steadily since the latter won general elections in January.
Fatah recognises Israel, but Hamas officially wants an Islamic state in Israel, the West Bank and Gaza. Its charter calls for Israel's destruction.
The plan Mr Abbas will put to a non-binding referendum is an 18-point programme agreed by various faction members jailed by Israel.
It sets out formal Palestinian claims to an independent state on land occupied by Israel in 1967, as well as the right of all Palestinian refugees to return to former homes inside Israel.
Thousands of Palestinians left their homes following the establishment of Israel in 1948.
The document calls for continued resistance within lands occupied by Israel in 1967, suggesting that attacks inside internationally-recognised Israel would end.