The Pentagon is moving toward providing Ukraine with bigger, longer-range radar to help it counter artillery being used by Russia-backed rebels, as U.S. military officials signal a growing willingness to bolster the country’s defenses.

The proposal still requires approval from the White House, which is considering another package of nonlethal assistance for Ukraine. The deliberations are taking place alongside rising pressure on Washington to better help Kiev counter a rebellion that continues to regularly claim lives, despite...