Israel acknowledged striking a radar installation near Tehran hours after the start of a ceasefire on Tuesday, in retaliation for Iranian missile launches, but said it had refrained from further attacks beyond that after President Donald Trump spoke with Prime Minister Benjamin Netanyahu.

The prime minister's office acknowledged the strike in a statement after Trump publicly expressed frustration that Israel had launched strikes on Iran after the ceasefire agreement was reached but before it took effect.

Trump, who had announced the ceasefire overnight, also criticized Israel's plans to respond militarily to an alleged Iranian violation of the ceasefire.

Tehran has rejected accusations that it breached the truce, which was meant to start at 7 a.m Israeli time, and instead said Israel had continued its attacks on Iran for an hour and a half after the ceasefire came into effect.

Netanyahu's office said that Israel had carried out a strike in Tehran targeting Iranian security forces at 3 a.m., four hours before the ceasefire was due to start.

Trump, speaking to reporters in Washington, said that he "didn't like the fact" that Israel had "unloaded" right after reaching the ceasefire.

An Iranian missile strike on Beersheba in Israel's south killed four Israelis on Tuesday morning. Netanyahu's office said that attack had been launched before the truce started.

But it also accused Iran of launching a single missile six minutes after the ceasefire went into effect and firing another two missiles around three and a half hours later, at about 10:25 a.m. Those missiles were either intercepted or fell in open areas without causing casualties or damage to property, Netanyahu's office said.

In retaliation, the Israeli air force destroyed the radar installation near Tehran, it said.

Israel refrained from carrying out other strikes on Iran after a conversation between Trump and Netanyahu, the prime minister's office said, without specifying if the conversation had taken place before or after the attack on the radar station.

The prime minister's office did not immediately respond to a request for comment on the sequence of events.