The U.S. military continued its blockade of Iranian ports on Tuesday, turning up the economic pressure as mediators in Pakistan raced to lock down another round of peace talks. President Donald Trump told the New York Post on Tuesday that a second round of negotiations could happen over the next two days, leaving a tight timeline for a potential deal before the current ceasefire expires on April 22. Trump announced a naval blockade, which took effect on Monday, after a first round of talks with Iran came up short over the weekend. The stated goal is to cut off Iran's access to world markets and open up the Strait of Hormuz, the crucial oil shipping route that Tehran has largely closed down since the war started. U.S. Central Command said more than 10,000 American service members were helping to enforce the blockade, alongside over a dozen warships and dozens of aircraft. "During the first 24 hours, no ships made it past the U.S. blockade and 6 merchant vessels complied with direction from U.S. forces to turn around to re-enter an Iranian port on the Gulf of Oman," CENTCOM added in an update on Tuesday. Iran appears to be holding its fire so far after previously threatening to retaliate against other ports in the region. Fighting continues on another front between Israel and Hezbollah, an Iran-backed militant group, in Lebanon. Meanwhile, diplomats from Lebanon and Israel held their first high-level meeting since 1993 on Tuesday.U.S. Secretary of State Marco Rubio, who also attended the discussions in Washington, D.C., said diffusing long-standing tensions would take more than one day. "It's a historic gathering that we hope to build on, and the hope today is that we can outline the framework upon which a permanent and lasting peace can be developed," Rubio said. A joint statement later released by the U.S. State Department described the discussions as "productive," adding that all sides have "agreed to launch direct negotiations at a mutually agreed time and venue." "The United States affirmed that any agreement to cease hostilities must be reached between the two governments, brokered by the United States, and not through any separate track," the statement added. Yechiel Leiter, the Israeli ambassador to the U.S., expressed confidence that they would be able to work with Lebanon's government to address security threats from Hezbollah. "We discovered today that we're on the same side of the equation. That's the most positive thing we could have come away with. We are both united in liberating Lebanon from an occupation power dominated by Iran called Hezbollah," Leiter told reporters. Lebanese Ambassador to the U.S. Nada Hamadeh Moawad underscored "the principles of territorial integrity and full state sovereignty." She also called for a ceasefire and "concrete measures to address and alleviate the severe humanitarian crisis that the country continues to endure as a result of the ongoing conflict." Hezbollah was not represented at Tuesday's meeting and has said that it would not abide by any agreement struck between the two governments. Hezbollah appeared to step up its attacks on northern Israel as the discussions got underway on Tuesday. Israeli strikes have killed a total of 2,124 people during the six-week war, according to Lebanon’s health ministry said.