Qurei's announcement came on Thursday in response to previous statements by senior officials in the ruling Palestinian Fatah Party indicating that the elections could be postponed.
Although no such decision has been announced, party members and advisers said that there are two reasons for seeking a delay.
A Fatah official in Rafah, Luay Abdu, told Aljazeera.net on Thursday that pushing back elections was necessary because of the difficulties created by Israel's expected withdrawal in August.
"While it's true we have had municipal elections earlier this year, the measures Israeli occupation forces are creating in preparation for their withdrawal - curfews, limited travel - are making a fair vote in July increasingly unlikely."
The official also noted that the Palestinian parliament had not yet passed a new election law. "That makes it difficult to conduct elections on time," Abdu said.
And a senior aide to Palestinian president Mahmoud Abbas has also called for the delay, but for a different reason.
Fatah leaders face an uphill task
as election date approaches
Tayeb Abd al-Rahim told Associated Press on Thursday the party was heading for defeat if it goes to elections in July.
Polls show Palestinian voters are fed up with corruption and inefficiency in the Palestinian government.
And the electorates' dissatisfaction may mean Abbas leading his Fatah Party to defeat.
According to Abd al-Rahim, Fatah leaders would have a better chance if the election was held after Israel's withdrawal from Gaza this summer - something Abbas can claim as an achievement - and after a party convention in August would usher some younger, reform-minded candidates into key positions.
But Hamas rejects any suggestion of delay, pointing out that elections under Israeli occupation were possible as previous ballots had proved.
Spokesman Sami Abu Zahra told Aljazeera.net that a failure to hold elections on time would mean the end of the 8 February ceasefire with Israel.
Hamas won three of the biggest
races in recent local elections
"Holding elections on time was part of the [Sharm al-Shaikh] agreement. Failure to stage elections on time would have serious implications," he said.
The 8 February Sharm al-Shaikh truce has reduced the number of Israeli deaths to zero, however about 20 Palestinians have died in the same period - with 10 of the victims being children.
ِAnd Hamas' spokesman in the West Bank, Hasan Yousuf, told Aljazeera.net the Islamist organisation strongly rejected any postponement. "This constitutes a flagrant usurpation of the Palestinian people's will," he said.
He accused "certain interest groups" of wanting to "tailor democracy according to their whims, desires and parochial interests".
Earlier this week, a Palestinian official at the PA Ministry of Information told Aljazeera.net's Khalid Amayreh that US Secretary of State Condoleezza Rice privately suggested the PA should do something to prevent Hamas from achieving an election victory.
The last time Palestinians voted in parliamentary elections was in January 1995 under terms of an interim peace deal with Israel.
Palestinians have tried to schedule new elections several times, but attempts were usually cancelled as free elections could not be held with Israeli troops in control of the roads and towns.
Last month, Hamas officials said they were approached by Abbas with an offer to agree to postponing the election until the end of the year, and that in exchange they would receive jobs in the current cabinet.
"Holding elections on time was part of the [Sharm al-Shaikh] agreement. Failure to stage elections on time would have serious implications"
Sami Abu Zahra,
Hamas leaders said they rejected the plan. And in recent months, Hamas has participated in three rounds of municipal voting in the West Bank and Gaza, posing a strong challenge to Fatah.
In local elections last week, Fatah won control in a majority of 83 towns and villages. However, Hamas won the three biggest races, in the towns of Rafah, Beit Lahiya and Qalqiliya.
Khalid Amayreh in the West Bank contributed to this report.