Opposition supporters have been camped out in central Beirut since December 1 calling for the government of Fouad Siniora, the Lebanese prime minister, to step down. Hezbollah says the campaign will remain peaceful.
In an interview with Hezbollah's al-Manar television station late on Monday, Kassem said: "The opposition forces will sit together and assess what happened in the last month ... study ideas proposed in the arena - whether there are horizons for solutions or not.
"Naturally, it has become clear that the horizons are not very open. Then [the opposition] will take a series of steps, actions."
Many Lebanese fear that the situation may turn violent. One anti-government protester has already been killed.
The protest has severely disrupted commercial life in central Beirut, where roads are closed and troops, armoured vehicles and razor wire protect the government's headquarters.
The opposition initially called for veto power in cabinet but has raised its demands to early parliamentary elections.
It has declared as illegitimate Siniora's government, which came to office in parliamentary elections after the withdrawal of Syrian troops in 2005.
Government leaders say the opposition is trying to stage a coup that would lead to more Syrian and Iranian influence in Lebanon. Hezbollah says Siniora's cabinet answers to the US government.
Kassem accused the government of wrecking an initiative by Amr Moussa, the Arab League secretary-general, to end the crisis - Lebanon's worst since its 1975-1990 civil war.
"The government factions believe time is on their side - that the opposition will tire. We say to them today the opposition will not tire and is staying in the street," Kassem said.
Anti-Syrian leaders say the opposition's real goal is to derail an international tribunal to try suspects in the assassination of Rafik al-Hariri, the former Lebanese prime minister, on February 14, 2005.
The anti-Syrian coalition believes that Syrian-backed opposition groups want to shield Damascus from prosecution. Syria denies involvement in the killing - the first in a series of assassinations of anti-Syrian figures.
Kassem said Hezbollah was concerned the tribunal had a political slant that reflected US designs. Washington, which brands Hezbollah a terrorist group, wanted the court formed quickly for its own purposes, he said.
Kassem reiterated Hezbollah's position that it supported the idea of the court, but said it wanted to discuss the details.
"We are scared of politicisation. Therefore we insist on discussion of the articles of the tribunal, one by one. The tribunal should be approved in the framework of a legitimate cabinet and not an illegitimate cabinet," he said.