"He has been saying that he will serve all Sudanese whether they voted for him or not," our correspondent said.
The election commission also announced that Salva Kiir, the leader of the former rebel Sudan People's Liberation Movement (SPLM), won re-election in the presidential poll in Sudan's semi-autonomous southern region.
Kiir, a former rebel commander, won 92.9 per cent of the 2,616,613 votes in the South, Alier, the commission chairman, said.
Sudan's elections were set up under a 2005 peace accord that ended more than two decades of north-south civil war and saw the formation of a power-sharing agreement between Kiir's SPLM and Bashir's National Congress Party (NCP).
The results followed widespread accusations of voter fraud and polling irregularities in the presidential, parliamentary and regional elections.
The main opposition parties decided to boycott some aspects of the polls, accusing al-Bashir of widespread vote rigging.
Hafez Mohammed, the director of Justice Africa, a research and advocacy group in Khartoum, said the fraud allegations of fraud have overshadowed the credibility of the results.
"The legitimacy [of al-Bashir's win] is questionable because of the withdrawal and the allegations of rigging that have absolutely dented the whole process of the election," he told Al Jazeera.
"That is going to be a serious problem facing the ability of the government to govern properly with authority."
The SPLM pulled out of parliamentary voting in most northern states and withdrew Yasser Arman as its candidate for the presidency.
Sadiq al-Mahdi, Sudan's former prime minister from the northern opposition Umma party, also withdrew, citing possible fraud.
Those decisions left little competition for al-Bashir, who has been in power for 22 years.
International observers from the European Union and the US-based Carter Centre had also criticised the polls, saying that the elections did not meet international standards.
Al Jazeera's Adow said attention was now focused on the reactions of Sudan's opposition parties.
"They are angry and saying this election has been fraudulent right from the beginning of registering voters up until now," he said.
"Some of them say they will be holding demonstrations and protests against what they call rigged elections."
Mubarak al-Fadil, the leader of the Umma Reform and Renewal part, told the Reuters news agency that the government had "cooked the figures".
"His campaign was conducted under one party system with all the foundations of a police state ... it was a farce," he said.
Ahmed Hussein, the spokesman for Justice and Equality Movement (Jem) in Darfur, also said his group would not accept the results.
"Things in our country are not going according to what the people of Sudan wanted. This is going to lead to tension and chaos," he said.
|Kiir, a former rebel leader, was re-elected president of Sudan's South [EPA]
The election results come less than a year before Sudan holds a referendum in January 2011 on the independence for the oil-producing south, a provision included as part of the 2005 peace accord.
Al-Bashir vowed to go ahead with the referendum, following Monday's results announcement.
"I assure [you] the referendum in south Sudan will take place on schedule," he said in an address broadcast on state television.
Al-Bashir also used his victory address to pledge greater efforts to reach a peace agreement in the country's western Darfur region, where the UN estimates that about 300,000 people have been killed in an ongoing conflict.
"I assure [you] ... that we will work for peace in Darfur," he said.
Al-Bashir is facing an arrest warrant from the International Criminal Court (ICC) for alleged war crimes and crimes against humanity in Darfur, though he has denied the charges.