The US top general late Monday warned Iran not to get involved in the crisis in Israel and said he did not want the conflict to the broaden, as Lebanese Hezbollah fired rockets onto northern Israel.

The White House earlier on Monday said that Iran was complicit even though the United States has no intelligence or evidence that points to Iran's direct participation in attacks in Israel by Palestinian Islamist group Hamas.

Asked what his message for Iran was, General Charles Q. Brown, the chairman of the Joint Chiefs of Staff, said: "Not to get involved."

Israeli shelling on Lebanon killed at least three Hezbollah militants on Monday, and Israel said one of its officers was killed during an earlier cross-border raid claimed by Palestinians in Lebanon.

The cross-border violence marked a significant expansion of a conflict between Israel and Palestinian militants in Gaza to the Israeli-Lebanese border further north.

Iran-backed Hezbollah and Israel fought a brutal month-long war in 2006.

"We want to send a pretty strong message. We do not want this to broaden, and the idea is for Iran to get that message loud and clear," Brown told a small group of reporters traveling with him to Brussels, in his first public comments since being confirmed to the job last month.

The US military is "surging" fresh supplies of air defenses, munitions and other security assistance to Israel to help it respond to an unprecedented weekend attack by Hamas.

On Sunday, the Pentagon announced that it was sending an aircraft carrier strike group closer to Israel.

"It sends a very strong message of support for Israel. But it's also to send a strong message of deterrence to contain broadening this particular conflict," Brown said.

He compared Hamas' actions to those of Islamic State militants.

Report by Reuters