Supporters of football star George Weah, who lost to former finance minister Ellen Johnson-Sirleaf, rampaged through Monrovia late on Sunday after Weah told them to fight for "liberation".
Johnson-Sirleaf was abroad and not due back until Friday.
Liberia's government held a crisis meeting on Monday to discuss the unrest, in which riot police surrounded Weah's party headquarters as protesters smashed car windscreens and pelted officers with rocks.
William Allen, the information minister, told reporters: "The government of Liberia has gathered from intelligence and security sources that there were some people plotting a coup. The security service is conducting an investigation into this report.
"There are two government officials who are said to be part of this plot. I cannot give you the details or their names because the investigation is still continuing."
Weah, a former striker with AC Milan who has a strong following among young Liberians, and his Congress for Democratic Change (CDC) party, say the polls were marred by cheating.
He won the first-round vote, but by too small a margin to claim outright victory. International electoral observers said that the elections were fair.
Weah told supporters at a rally at the weekend: "My fellow revolutionaries, liberation is a noble cause. We must fight to obtain it."
But in new remarks broadcast on his own King Radio station in Monrovia, he denied advocating violence. "I am not a violent man," he said. "I am not a rebel. Why should I stage a coup? ... I call on my supporters to remain calm."
Kabene Ja'neh, the justice minister, said the government would not tolerate any attempt to destabilise the country.
"Under our law, there can be no two presidents at a time," he said. "We want to make it very clear that no one individual or party will be allowed to derail this peace process."
Liberia is struggling to recover from an intermittent civil war that continually ravaged the country over 14 years until 2003.