BRUSSELS — At the end of a week when the European Union slapped Israel with financing restrictions to push it to resolve its conflict with the Palestinians, major European powers on Friday stepped up pressure to give Israel one of its long-sought demands: designating the Lebanese militant group Hezbollah as a terrorist organization.

The timing of the carrot-and-stick actions was coincidental, but they illustrated the bloc’s strategy of pushing forward with its own efforts to rein in Israeli actions that undermine the Middle East peace process — and to maintain good relations with Israel, understanding its unique security needs.

The approach has leading member states like Britain and France making a renewed effort to navigate deep divisions within the Union over the Middle East peace process, in which the United States’ role has long eclipsed that of the Union.

It may continue to do so. Analysts said the moves by Europe were unlikely to be a game changer in the region, a conclusion seemingly underlined on Friday when Secretary of State John Kerry announced possible Israeli-Palestinian talks in Washington as early as next week.