The ruling Cambodian People's Party (CPP) showed a lead in other provinces as commentators had expected. The CPP is tipped to win easily ahead of the royalist FUNCINPEC party and the SRP.
The incumbent prime minister, Hun Sen, is a former Khmer Rouge officer who fled the ultra-Maoist party at the height of the notorious "killing fields" purges in 1977.
Hun Sen returned to Cambodia with the 1979 Vietnamese invasion, which overthrew Pol Pot's brutal regime. He assumed power in a 1997 coup.
Unofficial results in the proportional representation vote showed the SRP was leading the CPP substantially in 10 communes out of Phnom Penh's 70 with the royalist FUNCINPEC party a distant third.
CPP sources told Agence France Presse that in the 10 communes the SRP had received 1,060 votes, the CPP 668 votes and FUNCINPEC 217 votes.
"With 14 percent of the total count done by early Monday we have seen that the opposition Sam Rainsy Party is leading in Phnom Penh city," Om Yintieng, a senior advisor to Prime Minister Hun Sen told AFP.
"But the (other) results have shown that the CPP is leading in the main provinces," he added.
The figures were for the total overall vote. No numbers were available for individual seats.
Rural voters stay with the government
The CPP's performance was markedly better in the countryside, particularly in the western province of Battambang where ruling party sources said it had garnered 510 votes, FUNCINPEC 160 votes while the SRP was trailing with 130 votes.
"I appeal to all national citizens to keep a highly responsible spirit, to keep calm and maintain social order."
-Cambodian prime minister Hun Sen
In remote northern Stung Treng province the CPP had received 142 votes, FUNCINPEC 59 votes and the SRP 16, first figures showed.
Communes are clusters of villages which represent the local government level in Cambodia. Ballots from 12,826 polling booths for the 123-seat National Assembly have been centralised for the count at 1,621 communes.
Premier appeals for continued calm
The election has taken place in an unprecedented climate of peace and security, and the premier has appealed to the population as well as the military, political parties and government authorities to maintain stability until the new government takes office.
"I appeal to all national citizens to keep a highly responsible spirit, to keep calm and maintain social order during vote-counting and when the results are officially announced," said Hun Sen in a statement released late Sunday.
"I wish to appeal to all government ministers, institutions and authorities at all levels, and the armed forces to continue being careful in fulfilling their duty and take all measures to strengthen stability, security and social order until the new government takes power," he said.
Such a comment indicated that Hun Sen was unlikely to tolerate public disorder nor heavy-handedness from the military should any unrest break out from disgruntled voters.
Sunday's elections took place virtually without incident in a marked departure from previous elections which have been marred by violence.
An explosion in the capital, which caused no injuries or damage, detracted only slightly from an overall calm throughout election day.