Results in the Ashanti and Volta areas have been disputed, and the Tain region, where the poll was delayed, will now vote on Friday.
Officials said the contest between the opposition's John Atta Mills and ruling party's Nana Akufo-Addo was so close one result could decide the outcome.
The BBC correspondent in Ghana says the further delay might heighten tensions.
New Patriotic Party (NPP) candidate Mr Akufo-Addo gained the most votes in the first round earlier this month but did not pass the 50% threshold needed for outright victory.
Electoral commission chairman Kwadwo Afari-Gyan said opposition National Democratic Congress (NDC) candidate Mr Atta Mills had won 50.13% of the vote, while Mr Akufo-Addo had taken 49.87%.
This means just 23,055 votes divide the two candidates, out of a total cast of some 9m.
"Results are so close that the result of the Tain constituency could affect the eventual winner," Mr Afari-Gyan said.
He said the results covered all 230 constituencies, except Tain in the Brong Ahafo region, which was unable to vote on Sunday because of a problem with voting materials.
According to the Daily Guide newspaper, the ruling party had accused electoral officials in Tain of stealing about 1,820 ballot papers, which they claimed were given to the opposition.
The district has some 53,000 registered voters.
The privately-owned Joy FM radio station reported that during the first round of the vote in Tain earlier this month, 30,000 electors turned out and awarded a narrow victory to Mr Atta Mills.
The commissioner, who has been stuck in behind-closed-doors wrangling with both parties in the capital Accra, said they would also use the delay to audit the disputed results.
The electoral commission headquarters was besieged for much of Tuesday by thousands of NDC supporters demanding their candidate be declared the winner.
Armed police and soldiers backed by water cannon trucks and an armoured personnel carrier kept the protesters behind barricades and at one point fired warning shots.
As tensions rose, party officials handed out ice cream and water to the crowds to calm them down.
Mr Atta Mills had earlier claimed victory, but the NPP said this was premature.
Shops closed early on Tuesday, with businessmen fearing that there could be looting once the result is announced.
The opposition has been disputing results awarded to the governing party from five constituencies in its stronghold of the Ashanti region.
It is understood turnout in one area was recorded at 99% - said by election experts to be unheard of - while there were also complaints dead people, children and foreign nationals had been listed among voters.
The NPP, meanwhile, said there had been widespread intimidation of its election agents in the Volta region and results from these areas would be challenged.
International observers have given the poll a preliminary clean bill of health and urged both candidates to accept the results.
Some 12.5 million people were eligible to vote in the election - the fifth since Ghana's return to democracy in 1992.
President John Kufuor is standing down having served two consecutive terms.
In the two previous elections he defeated Mr Atta Mills.
Mr Atta Mills served as vice-president under former leader Jerry Rawlings.
Monitors hope Ghana's poll can help salvage the tarnished image of constitutional democracy in Africa, after flawed elections in Kenya and Zimbabwe and military coups in Mauritania in August and in Guinea last week.
The stakes have been raised in these elections because Ghana has just found oil, which is expected to start generating revenue in 2010.