Iran has launched multiple waves of missiles at Israel, the Israeli military says, while an attack has been launched from Yemen for only the second time since the US-Israeli war began.
The military said two drones from Yemen were intercepted early on Monday but gave no further details.
Yemen's Iran-backed Houthi militia entered the war on Saturday, firing missiles at Israel, escalating a conflict that has engulfed the Middle East.
Israel's military said the Air Force was carrying out strikes on Tehran on Monday, targeting what it described as military infrastructure.
The latest attacks came a day after President Donald Trump said the US and Iran had been meeting "directly and indirectly" and that Iran's new leaders have been "very reasonable", and as more US troops arrived in the region.
Pakistan, which is acting as an intermediary between Tehran and Washington, said it was preparing to host "meaningful talks" in the coming days aimed at ending the month-long Iran war.
It was not clear whether the US and Iran had agreed to attend.
"I think we'll make a deal with them, I'm pretty sure, but it's possible we won't," Trump told reporters on Sunday as he travelled aboard Air Force One to Washington.
Trump said he thought the US had already accomplished regime change in Tehran after strikes killed the country's supreme leader and other top officials, but said twice that their replacements seemed "reasonable".
An initial Israeli strike on February 28 killed Iran's Supreme Leader Ayatollah Ali Khamenei, who was replaced by his son Mojtaba.
The war has spread across the Middle East, killing thousands, causing the biggest disruption ever to energy supplies and hitting the global economy.
Iran's parliament speaker, Mohammad Baqer Qalibaf, has accused the US of sending messages about possible negotiations while planning a ground invasion.
"As long as the Americans seek Iran's surrender, our response is that we will never accept humiliation," he said in a message to the nation.
The US Department of Defense has dispatched thousands of troops to the Middle East, giving Trump the option of launching a ground offensive.
Israel's military said it had launched more than 140 air strikes on central and western Iran, including Tehran, in the 24 hours to Sunday evening, hitting ballistic missile launch sites and storage facilities.
Iranian state media reported strikes had hit Mehrabad airport and a petrochemical plant in the northern city of Tabriz.
Four weeks of intense US-Israeli bombardment have failed to silence Iran's missile and drone batteries, with Kuwait on Monday reporting it had intercepted five drones in areas under its protection.
A chemical plant in southern Israel near the city of Beersheba was hit by a missile or missile debris on Sunday as Israel fended off multiple salvos from Iran.
Iran also continues its effective blockade of the Strait of Hormuz, which carries 20 per cent of global oil and gas shipments, spiking oil prices and spreading economic pain around the world.
Yemen's Iran-aligned Houthis joined the conflict on Saturday, launching their first attacks on Israel and raising the prospect they could target and block a second key shipping route, the Bab el-Mandeb Strait.
Stocks slumped in Asia on Monday as investors dug in for a protracted conflict, bringing a spike in inflation and the risk of recession to much of the globe.
Meanwhile, oil prices looked poised to extend their gains, with Brent headed for a record monthly rise.
Global airlines have begun to hike fares and cut capacity to cope with the surge in the oil price, but analysts warn the industry's ability to remain profitable might depend on whether consumers pull back on flying as energy costs threaten household budgets.
The majority of Americans are opposed to the war and a military escalation, which would risk a protracted crisis and likely weigh further on Trump's already low approval ratings ahead of the November midterm elections for Congress.
Israeli Prime Minister Benjamin Netanyahu has ordered the military to expand operations in southern Lebanon, citing continued rocket fire by Iran-backed Hezbollah militia.
Israel has said it will seize a chunk of southern Lebanon to create a "buffer zone" against Hezbollah, stoking fears among Lebanese of Israeli military occupation that could deepen instability and stoke further displacement.