Oil futures rallied by more than 3% on Tuesday as signs of an overall slowdown in U.S. crude production expected later in the year helped lift prices for the U.S. crude benchmark back above $60 a barrel. May oil output was at its highest monthly level in more than four decades, but production is expected to slow during the second half of the year, according to a monthly U.S. government report.

Traders also awaited other monthly reports due out this week, which will offer demand forecasts. Weekly U.S. inventory data are due later Tuesday and on Wednesday morning. Meanwhile, talk centered on easing the ban on U.S. crude exports intensified. July crude jumped $2, or 3.4%, to settle at $60.14 a barrel on the New York Mercantile Exchange. July Brent crude on London’s ICE Futures exchange rose $2.19, or 3.5%, to $64.88 a barrel. Both contracts settled at their highest since June 2. May U.S. oil production averaged 9.6 million barrels a day in May, the highest monthly level since 1972, according to the Energy Information Administration Tuesday. Output, however, is expected to decline from June through early 2016. The EIA also forecast 2016 output to average 9.27 million barrels a day — below its 9.43 million forecast for 2015.

Oil production from seven major U.S. shale plays is expected to fall by 91,000 barrels a day in July from June, according to a monthly EIA report released Monday. Still, Colin Cieszynski, chief market strategist at CMC Markets, pointed out that U.S. production declines are “being offset by even bigger increases in Saudi Arabia, Iraq and elsewhere — with Iran to come,” he said. If Iran reaches a final agreement with world powers over its nuclear program, sanctions on Iran are likely to be lifted, and the country has said it stands ready to boost oil production. OPEC will issue its oil report on Wednesday and the International Energy Agency’s report comes out Thursday, with both expected to offer demand forecasts.

Late Tuesday, the American Petroleum Institute will release its weekly U.S. oil inventory data, followed by the EIA Wednesday. Analysts polled by Platts forecast a decline of 1.6 million barrels. Media reports in recent days have also played up talk among analysts and politicians over lifting the 40-year-old ban on U.S. oil exports. There is “some chatter” that the Senate could soon vote “on policy regarding U.S. crude-and-gas exports to aid our allies and partners,” said Tyler Richey, analyst for the 7:00’s Report.