The U.S. has softened its position in talks on global bank-capital rules, easing a months-long deadlock with the European Union and boosting the chances of a deal.

The Federal Reserve, which leads the U.S. delegation in the Basel Committee on Banking Supervision, is ready to compromise on the level of a disputed output floor, according to two people with knowledge of the talks. The floor is a blunt check on firms' use of their own statistical models to measure asset risk, part of the process for determining their capital requirements.

A wide gap still remains between the U.S., which has long been skeptical of banks' internal models, and Europe, which insists the models provide more accurate assessments in many cases. On Tuesday, Raimund Roeseler, an executive director at BaFin, Germany's banking supervisor, told reporters that a deal at the Basel Committee's next scheduled meeting in mid-June is unlikely because "we're still too far apart."

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