Ethiopia is pinning its hopes of economic development and power generation on the dam. Egypt relies on the river for as much as 90% of its fresh water and sees the dam as an existential threat. Sudan is concerned about the operation of its own Nile dams and water stations.
The ministers, meeting in Qatar, agreed on "steps to be taken gradually" to support Egypt and Sudan in the dispute, Qatari Foreign Minister Mohammed Bin Abdulrahman Al-Thani told a news conference, without giving details.
The Arab states called on Ethiopia to negotiate "in good faith" and refrain from any unilateral steps that would harm Egypt and Sudan.
Such steps included completing the second phase of filling the dam's reservoir in the rainy season this year without an agreement on filling and operating the dam, the Arab League said in a statement.
Ethiopia rejected the Arab League resolution in its entirety, its Foreign Ministry said in a statement.
The country previously rejected calls from Egypt and Sudan to involve mediators outside the African Union.
Sudan and Egypt had already agreed this month to work together on all levels to push Ethiopia to negotiate "seriously" on an agreement, after African Union-sponsored talks remained deadlocked.
The two countries, which are downstream from the Grand Ethiopian Renaissance Dam, called on the international community to intervene. Aboul Gheit described the water security of Egypt and Sudan as an integral part of Arab national security.
Sudan said on Monday it was open to a partial interim agreement on the multibillion-dollar dam, with specific conditions.
Tuesday's meeting was the first such gathering of Arab states that Qatar has hosted since Saudi Arabia and its allies imposed a boycott on Doha in mid-2017 over accusations that Qatar supported terrorism, a charge it denies.
Saudi Arabia, the UAE, Bahrain and Egypt agreed in January to restore diplomatic, trade and travel ties with Doha.