Iran said Thursday that new sanctions imposed by the United States had violated its nuclear deal with world powers and that the country would respond, piling pressure on President Hassan Rouhani as he began his second term.
On Tuesday, during a State Department briefing, Tillerson revealed that he and the president were now discussing how they can use the existing deal.
"We call on Iran to immediately cease all activities related to ballistic missiles created to be capable of delivering nuclear weapons, including launches using such ballistic missile technology", the four powers wrote in their letter.
He noted that imposing fresh sanctions on Iran is an attempt to reduce Tehran's benefits from the nuclear accord and to negatively affect its "successful implementation".
Trump, who during his election campaign called the nuclear agreement - negotiated under his predecessor Barack Obama - "the worst deal ever", signed the new sanctions into law along with measures against Russian Federation and North Korea.
There was no immediate comment from Iran's United Nations mission.
Iran's action was, the four countries said, a violation of UN Security Council Resolution 2231, which calls on Iran not to undertake ballistic missile activity as part of its commitments under the 2015 nuclear deal.
Iran says its missiles are purely defensive and could not carry nuclear arms because the country has promised not to develop them.
"In our eyes, the JCOPA has been violated (by the United States), and we will give deserved response", Iran's Deputy Foreign Minister Abbas Araqchi was quoted as saying.
"There are a lot of alternative means with which we use the agreement to advance our policies and the relationship with Iran, and that's what the conversation generally is around with the president as well", he added.
"We will never accept isolation", Rouhani said as he was sworn in in front of top political and military officials.
House Speaker Paul Ryan said Trump's signing of sanctions legislation sends a powerful message to United States foes that "they will be held accountable for their actions".
Simorgh (Phoenix) rocket, which Iran launched into space on July 27. The US, however, has prevented the deal from fully yielding. The news agency says senior officials from 92 countries are in Tehran for an oath-taking ceremony Saturday.
In attendance, according to Iran's state-run Islamic Republic News Agency (IRNA), is North Korea's second-most powerful leader, Kim Yong-nam.