PHOENIX (Reuters) - Arizona teachers said on Tuesday a proposed budget deal between the governor and state lawmakers to raise their pay did not go far enough, but pledged to end a four-day strike and return to work on Thursday if it passed the legislature.

Participants take part in a march in Phoenix, Arizona, U.S., April 30, 2018 in this picture obtained from social media. Twitter/@MR_GEARING/via REUTERS

Arizona Governor Doug Ducey said earlier on Tuesday he hoped to sign the agreement as early as Wednesday and end a walkout that kept most of Arizona’s 1.1 million public school students out of class for a fourth day.

“The war is not over but we’ve won an important battle, to move the legislature this far,” Noah Karvelis, a union organizer and music teacher, said at a news conference.

The walkout in Arizona followed similar actions by teachers in West Virginia, Kentucky and Oklahoma, which were the first statewide U.S. teacher work stoppages since the 1990s. All four states have Republican governors and Republican-dominated legislatures.

Teachers have demanded that states reverse salary and funding constraints imposed when tax revenues ran short during the 18-month U.S. recession that ended in June 2009.

Conservative groups such as Phoenix’s Goldwater Institute think tank have threatened to sue school districts over what it calls an “illegal strike” by public employees who are not allowed to strike under Arizona law.

Red-clad teachers packed the House of Representatives Appropriations Committee room in the state Capitol in Phoenix and registered to address lawmakers when budget negotiations on education funding begin on Tuesday afternoon.

But Ducey said in a letter to teachers released to the public on Tuesday morning that he and lawmakers were “very close to passing a significant budget investment into K-12 education.”

The deal would increase teachers’ pay 20 percent by 2020 and provide an extra $371 million in school funding over five years.

Educators have also called for higher pay for support staff and a promise that Arizona’s legislators will enact no new tax cuts until the state’s per-student funding level is brought up to the national average.

Arizona’s teacher salaries rank among the lowest in the country.

Ducey said his budget proposal would allow school leaders flexibility to spend funds to improve school facilities and increase support staff pay.