A hospital in Tehran was "targeted by a rocket attack" overnight Thursday into Friday, a spokesperson for the Iranian Ministry of Health said.

This is the third hospital "to come under attack" since the beginning of Israeli strikes in the last week, according to the spokesperson.

Israel has also attacked six ambulances and a health center, according to the ministry.

A residential building in Beersheba in southern Israel was damaged by an Iranian missile early Friday morning, according to emergency services.

Five people were treated for minor injuries after the strike, authorities said.

Meanwhile, the IDF said it conducted multiple strikes in Tehran overnight, targeting missile production sites and the headquarters for Iran's nuclear research program.

The Israel Defense Forces has issued an "urgent warning" to those living in Kolesh Taleshan, a small village in northern Iran.

"The IDF is expected to operate in your area, just as it has over the past few days throughout Iran, to strike military infrastructure," the notice stated, urging people to evacuate immediately.

Iran also issued an evacuation order earlier Thursday directed at Israel's Channel 14 news station, Iranian media said. The order comes days after Israel targeted Iran's state TV live on air, claiming it was the heart of the regime's communications.

While there are no concrete signs that the Iranian regime is any more likely to cut a deal now than they were at the beginning of the week, administration officials are pitching the president’s two-week timeline as a chance to let diplomacy play out.

"Trump is not a warmonger," one senior official told ABC News. "He wants to give the Iranians some room to come to their senses."

Special Envoy for the Middle East Steve Witkoff and Iran’s Foreign Minister Abbas Araghchi have been in communication during recent days, but as of now, there are no plans for the two to meet, another official said.

Officials have also pitched Trump’s move to give the Iranians breathing room as necessary because of the heavy losses sustained among its senior leadership and nuclear policy experts who would be involved in the making and implementing of any deal.

European diplomats are set to hold talks with Araghchi in Geneva over the weekend. But some administration officials say they don’t see a whole lot of promise in the talks, seeing the Europeans as having a weak track record when it comes to handling Iran.

Israeli Prime Minister Benjamin Netanyahu and his hawkish compatriots have long seen negotiating with the Iranian regime as a fool’s errand. And while Netanyahu may say the Israelis don’t need any help to accomplish their operational goals in Iran, at the very least, it would make it much easier.

However, even though Israeli officials have been pushing their case plenty, the "special relationship" between the country and the U.S. doesn’t translate to leverage over the Trump administration.

-ABC News' Shannon Kingston