The incumbent, Levy Mwanawasa, called for calm but said police would deal firmly with those trying to "sabotage" the vote.
Mr Mwanawasa said the poll was free and fair but the authorities have delayed announcing the result for 12 hours for security reasons.
The president surged ahead in vote counting on Sunday.
Mr Mwanawasa's main challenger, Michael Sata, has warned of severe consequences if his protests about vote rigging are ignored.
Appeal for calm
In the capital Lusaka, witnesses said protesters looted a supermarket owned by South African retailer Shoprite and other shops in three townships as unrest spread.
Opposition supporters blocked streets with burning tyres and hurled stones at police, who fired back volleys of tear gas.
Mr Mwanawasa denied charges by Mr Sata, that the ruling Movement for Multiparty Democracy (MMD) conspired with election officials to rig the vote.
"It is clear that some political parties want to cause confusion and I ask all peace loving Zambians to say no to violence," Mr Mwanawasa said in an address on state television and radio.
"I want to appeal for calm and peace. The law enforcement agencies will deal firmly with all troublemakers and those who want to sabotage the elections," he added.
"It will not do to start questioning the results of the elections," Mr Mwanawasa.
Peaceful voting
The dramatic turn of events contrasted with orderly voting on Thursday in what poll observers described as a model African election.
The Southern African country is used to accusations of vote fraud, most recently in the 2001 elections that brought Mr Mwanawasa to power.
But Zambia has largely escaped the political violence that has dogged many other African countries.
Opposition leader
Mr Sata has praised the controversial land reform policies of Zimbabwe's Robert Mugabe and pledged to get tough with Chinese investors.
The former cabinet minister had looked set to trounce Mr Mwanawasa, who has won praise from international donors for his economic policies but struggled to win support among the poor.
But Mr Sata, who enjoys strong support in Zambia's key copper-producing region, slid to third place today. Mr Sata said more than 400,000 ballots had been spoiled or stolen.
Partial results from the electoral commission gave Mr Mwanawasa 42 per cent of votes counted, compared to 28 per cent for Hakainde Hichilema of the United Democratic Alliance and 27 per cent for Mr Sata, of the Patriotic Front.