Hezbollah, which fought a devastating war with Israel in 2006, stands a chance of winning the majority of seats in parliament in the polls and such a scenario would likely force the US to rethink its strategy towards Lebanon.
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".
"Already a message has been put out on a televison network owned and operated by Hezbollah saying this is clear meddling in Lebanon politics by the United States," he reported.
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".
Following his meeting with Sleiman, Biden told reporters: "I do not come here to back any party."
He said he had been asked by Barack Obama, the US president, to "demonstrate to you and the people of Lebanon our commitment to Lebanon".
But Hezbollah criticised Biden's visit as evidence of US meddling in Lebanon and denounced American support for Israel.
"The high American interest in Lebanon raises strong suspicion as to the real reason behind it, especially since it has become a clear and detailed intervention in Lebanese affairs," Hezbollah said in a statement.
Biden said the Lebanese people alone "should choose their leaders" and that the "sovereignty of Lebanon cannot will not be traded 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.
'Independent and sovereign'
Simon Karam, Lebanon's former ambassador to Washington, said the visits by Biden, and an earlier one by Hillary Clinton, the US secretary of state, last month could signal a shift in US policy in Lebanon.
|Hezbollah denounced Biden's visit as evidence of US meddling in Lebanon [AFP]
"I think the United States is hedging its bets on the eve of this new term in Lebanese political life and signalling strongly that they will be investing in state institutions first and among these institutions, in the president," he told the AFP news agency.
Clinton made a brief stop in Beirut, the capital, in April where she expressed Washington's support for a "free, independent and sovereign" Lebanon.
She said that the forthcoming election should be held without intimidation or outside interference.
A senior state department official travelling with her said at the time: "If Hezbollah wins [the June vote], we will have to look at the composition of the government, and particularly at the programme, to evaluate ... what we are going to do in Lebanon."
The US is at loggerheads with Damascus and Tehran over their support of Hezbollah, which Washington has branded a "terrorist" organisation.
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.
The US administration under Obama has also made efforts to mend ties with the Arab world, including Syria and Iran.