With eight states and the capital Abuja declared, President Jonathan’s People’s Democratic Party (PDP) has a lead of about 20,000 votes.
Final results in the closely contested poll are due Tuesday.
The US and UK in a joint statement expressed concern over possible “political interference” in the count.
“So far, we have seen no evidence of systemic manipulation of the process,” said the statement from UK Foreign Secretary Philip Hammond and US Secretary of State John Kerry.
“But there are disturbing indications that the collation process, where the votes are finally counted, may be subject to deliberate political interference.”
Nigeria’s election commission (Inec) dismissed these fears, with a spokesman telling the AFP agency “there is absolutely no basis” to talk of meddling.
Of the nine regions announced, the PDP has taken four, with 2,322,734 votes, and Gen Buhari’s All Progressives Congress (APC) taking five, with 2,302,978 votes.
Police in the battleground Rivers State have used teargas against female opposition protesters who were attempting to lodge complaints with election officials of alleged rigging.
Voting spilled into Sunday in some parts of Nigeria after problems were encountered with new electronic card readers.
President Jonathan was among those whose registration to vote was delayed by the technology, which was introduced to prevent fraud.
The PDP, which had opposed the card readers, called it a “huge national embarrassment”.
Election commission chief Attahiru Jega said only a fraction of the 150,000 card readers being used nationwide had failed.
Two main presidential candidates: Muhammadu Buhari, All Progressives Congress (APC), Muslim northerner, ex-military ruler, fourth presidential bid; and Goodluck Jonathan, People’s Democratic Party (PDP), Christian southerner, the incumbent.
Years of military rule ended in 1999 and the PDP has been in power ever since Nigeria is Africa’s largest economy and leading oil producer With a population of more than 170 million, it is also Africa’s most populous nation.
The presidential and parliamentary elections had been delayed by six weeks because of the insurgency by Boko Haram militants.
The Islamists attacked polling stations in north-eastern states, with a curfew declared in Bauchi State after fighting between the security forces and the group.
The UN gave an upbeat assessment of the vote on Sunday, with Secretary General Ban Ki-moon praising the “determination and resilience” of Nigerian voters, despite the reports of attacks by Boko Haram and others.
His comments were echoed by the regional bloc Ecowas, which urged Nigerians to accept the result.
The PDP has dominated Nigerian politics since 1999, but the APC is viewed as a serious challenge.
Voters are also electing members of the house of representatives and the senate.