However, populous states such as Lagos and Rivers are yet to declare.
With just over half of Nigeria's states declared, Gen Buhari's All Progressives Congress (APC) was reported to be ahead by some two million votes.
More results are due to be announced from 10:00 local time (09:00 GMT) on Tuesday.
Nigeria's election commission (Inec) suspended its declarations late on Monday night, after giving the results for 18 states and the capital Abuja.
President Jonathan's People's Democratic Party (PDP) gained 6,488,210 votes and Gen Buhari's APC party received 8,520,436 votes.
Several key states have yet to declare in the south, where Mr Jonathan, a southerner, enjoys strong support, .
The candidate with the most votes will only avoid a run-off if they gain at least 25% of the votes in two-thirds of Nigeria's 36 states.
The BBC's Will Ross in Abuja says that at this point, neither side is mentioning the possibility of losing the election.
Our correspondent says that international observers have broadly praised the conduct of the vote but there has been some concern over possible efforts to rig the outcome during the count.
Nigeria's election process: Key facts
- Candidate with the most votes is declared the winner in the first round
- The winning candidate also needs at least 25% of the votes in two-thirds of Nigeria's 36 states
- If there is no outright winner, the law says a run-off election must be held within seven days
- Victory in a run-off election is by simple majority
The US and UK have expressed their concerns over possible "political interference" during the count, in a joint statement.
A spokesman from Inec dismissed these fears, saying that "there is absolutely no basis" to talk of meddling.
Authorities in the undeclared Rivers State reportedly announced a curfew on Monday night after protests over alleged vote rigging.
Earlier, police in the state used teargas against female opposition protesters who were attempting to lodge complaints with election officials.
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.
Election commission chief Attahiru Jega said only a fraction of the 150,000 card readers being used nationwide had failed.
Nigeria at a glance:
- 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.
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 PDP has dominated Nigerian politics since 1999, but the APC is viewed as a serious challenge.
CREDIT: BBC
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