Lebanon's Western-backed governing coalition and the opposition, who are led by Shia group Hezbollah and backed by Syria, have failed to reach a deal to end the country's political deadlock.
"The United States believes a show of support is important for regional stability," said the senior official.
"We are very concerned about the situation in Lebanon. It has dragged on very long."
Admiral Michael Mullen, chairman of the Joint Chiefs of Staff, said the decision to send the warship should not be seen as threatening to any particular country.
has increased pressure on Syria
in recent weeks, targeting more individuals with sanctions.
Hassan Fadlallah, a Lebanese MP from Hezbollah, called the US decision to position the warships off the coast "an attempt to spark tension".
"The American administration has used the policy of sending warships to support its allies in Lebanon before, and that experiment failed and backfired," he said.
"We don't succumb to threats and military intimidation practised by the United States to implement its hegemony over Lebanon."
Richard Murphy, a former US ambassador to Syria, told Al Jazeera that the move was a sign that the US did not know what to do about Lebanon.
"It is gunboat diplomacy. I think it would be more useful for the US to find a way to engage with the conflicting parties in Lebanon.
"We have no dialogue with Syria and this is a moment for dialogue."
A US defence official said the USS Cole, a guided-missile destroyer, left Malta on Tuesday and was headed toward Lebanon, adding it would not be stationed within visible range of Lebanon but "well over the horizon".
Seventeen US sailors were killed in October 2000 when the USS Cole was attacked off the coast of Yemen by al Qaeda fighters.
Asked whether George Bush, the US president, had given the order, Gordon Johndroe, the White House spokesman, said: "The president is concerned about the situation in Lebanon and discusses the issue regularly with his national security team."
Lebanon's presidential elections were postponed again this week to March 11 from February 26, the 15th such delay, after rival leaders failed to reach a deal.
The opposition wants enough seats in a new government to give it veto power over cabinet decisions, a plan rejected by the governing March 14 bloc.
The ruling March 14 bloc and the opposition have been locked in a bitter power struggle since November 2006, when Hezbollah and its allies pulled its members out of the cabinet.
The country has been without a president since November when Emile Lahoud, who was supported by Syria, stepped down in the midst of the worst political crisis since the country's 1975-1990 civil war.
The deadlock has threatened to degenerate into new sectarian violence and continues to affect inter-Arab relations in the run-up to an Arab League summit in Syria next month.