"We are very concerned about Lebanon. That is one of our concerns over the coming weeks. We think it's very important that tribunal does its work," Hague said in an interview broadcast on Britain's Sky News television.
"I've announced an increase in the British funding for that tribunal, as did the United States with their funding, to make clear that it must go ahead, that justice must proceed in Lebanon for people to have any confidence in its future," he added.
Lebanon and Sudan were the "two areas in January that are most obvious at this stage to watch for a political crisis or an outbreak of violence," Hague said, referring also to the January 9 referendum on south Sudan's separation from the north.
"So across the international community we must be ready to do everything we can to assist with those countries," he added.
"We're in close consultation with the Government of Lebanon and with our allies about this."
The United States last month made a $10 million contribution to the tribunal. Britain has donated one million pounds ($1.5 million).
France said that the latest grant brings its total contribution to the tribunal to 4.5 million Euros since the inquiry began in 2007.
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