Worried that competitors could permanently secure a larger share of one of the most valuable export markets for U.S. meat and crops, agricultural groups are urging Trump administration trade negotiators to move swiftly to secure a bilateral trade agreement with Japan.

Leading ag groups, including the American Farm Bureau Federation, sent a letter last week to U.S. Trade Representative Robert Lighthizer highlighting the importance of keeping American farmers on a level playing field in the Japanese market. Competitor’s trade deals, they said, are putting a broad spectrum of U.S. farmers at a...