But Darfur's anti-government groups quickly dismissed the government move, calling it "insincere".
Past ceasefires announced by Khartoum throughout the five-year conflict in Darfur have collapsed.
The Sudan People's Forum, a platform of government and opposition figures, called for the ceasefire.
However, al-Bashir did not pledge to release Darfuri political prisoners, as recommended by the forum.
He further said that the ceasefire attempt was intended to provide a platform for government negotiations with the oppostion armed groups.
|Al-Bashir has stopped short of agreeing to release Darfuri political prisoners [AFP]
A peace conference in Qatar is scheduled for the end of the year, but opponents of the government have not yet made a firm commitment to attend.
At least 300,000 people have been killed and more than 2.2 million have been displaced since fighting began in Darfur in 2003, the UN says.
Khartoum has dismissed the UN estimates, saying that 10,000 people have died as a result of the conflict.
Thousands of non-Arab Darfuris are living in refugee camps, seeking shelter from Janjawid fighters.
The latest move by al-Bashir comes four months after the chief prosecutor of the International Criminal Court (ICC) demanded an arrest warrant for him on 10 counts of genocide, war crimes and crimes against humanity in Darfur.
Sudan has rejected the ruling of the court and in recent months has tried to persuade the UN Security Council to invoke a one-year suspension of any legal proceedings against al-Bashir.
Gibril Ibrahim, an adviser to the chairman of the Sudanese Justice and Equality Movement (Jem), one of the anti-government groups in Darfur, told Al Jazeera that they doubt whether al-Bashir is serious about a lasting ceasefire.
"I can't say we actually rejected the ceasefire but we do think that Bashir does not mean it. This is not the first time that the regime has declared a ceasefire," Ibrahim said on Wednesday.
"First, we need a creation of peace before any negotiations. We need to see the release of all the Darfurians [political prisoners]. We want to see real peace on the ground and in the [refugee] camps."
Jem wants to see a "serious" effort towards a lasting ceasefire by the Sudanese government before formal negotiations can get under way, he said.
Ibrahim accused al-Bashir of using the ceasefire declaration as a strategy to launch a crackdown on armed opposition groups.
"Disarmament of the various movements can only be done via a peace agreement," he said.
"By saying that he wants to disarm the Janjiwid, he is trying to bypass the ceasefire that he is declaring.
"Actually, he is going to fight, under the pretext that he is going to disarm this or that group."