Biden insisted his trip to Beirut to meet political leaders was not aimed at influencing the outcome of the elections.
"I did not come here to back any institution or political party," he said.
Biden vowed that the Lebanese people alone "should choose their leaders" and that the "sovereignty of Lebanon cannot not be traded away".
Al Jazeera's Todd Baer in Beirut said the visit was "significant because of the timing" and that the Hezbollah-led opposition "is not taking this [visit] too lightly".
Baer said the US was "deeply concerned" about the outcome of the election and that it "needs a stable Lebanon in order to pursue the Middle East peace initiative".
Biden said the Lebanese stand to benefit from Arab-Israeli peace and called for the isolation of opponents of this process, while repeating America's commitment to a comprehensive settlement.
"Lebanon has suffered terribly from war and we have a real opportunity now ... for peace," he said.
"I urge those who think about standing with the spoilers of peace not to miss this opportunity to walk away."
For his part, Sleiman said that he had told Biden "the Middle East conflict cannot be resolved at the expense of Lebanon".
"We also reiterated the importance of endeavours to reach a comprehensive lasting resolution to all the conflicts in the Middle East, " he said.
The US is at loggerheads with Damascus and Tehran over their support of Hezbollah, which Washington has branded a "terrorist" organisation.
The US has provided Lebanon with more than a billion dollars in assistance since 2006, including $410m to the military and the police.
At the airport before leaving the country, Biden reviewed a display of the military hardware the US has provided to Lebanon and said the US was "committed to meeting your army's needs".
Hezbollah criticised Biden's visit, saying Washington was "meddling" in Lebanese affairs and denounced American support for Israel.
"We call on all Lebanese, regardless of their political views, to rise up against such meddling which represents a flagrant violation of Lebanese sovereignty," Hassan Fadlallah, a Hezbollah MP, said.
While the US vice president was still in Beirut, Hezbollah held a mass rally in the southern city of Nabatiyeh to mark the 2000 departure of Israeli forces from the area.
Hassan Nasrallah, the Hezbollah leader, addressed the crowds via video from his hiding place in south Beirut.
He said the visits by Biden and Hillary Clinton, the US secretary of state, a month ago raised "strong suspicion and amounted to a clear and detailed interference in Lebanon's affairs."
Hezbollah officials say they have received assurances that the West does not envisage imposing the same sort of boycott it slapped on the Palestinians when a Hamas-led government took power in Gaza after an election in January 2006.
Biden, who arrived in Beirut on Friday, also met Fouad Siniora, the prime minister, and Nabih Berri, the parliament speaker.
The US administration under Barack Obama, the US president, has also made efforts to mend ties with the Arab world, including Syria.