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By JESS BRAVIN

WASHINGTON—The Supreme Court on Monday agreed to decide whether an aggressive Arizona statute targeting illegal immigrants interferes with federal law, entering another high-profile dispute between the Obama administration and conservative state governments.

Among other provisions intended to drive illegal immigrants from the state, the 2010 Arizona measure, known as SB 1070, requires police to arrest people they stop whom they suspect of being foreigners without authorization to reside in the U.S. Federal courts have blocked much of the Arizona measure from taking effect, agreeing with the Justice Department that it undermines federal authority over immigration.

The court is likely to hear the case by April and issue a decision before July. That i's the same time it is expected to rule on the president's 2010 health-care overhaul, which conservative activists and Republican leaders from 26 states contend exceeds federal authority.

The scheduling positions both cases for a significant role in next year's presidential and congressional elections—and could make the Supreme Court, certain to be criticized by the losers in each case, itself an issue. Four of the nine justices are in their 70s, suggesting the next president could have at least one vacancy to fill on the closely divided court.

In yet another case with political ramifications, the justices decided late Friday to rule on the deference that federal courts evaluating redistricting plans under the Voting Rights Act of 1965 should pay to state legislatures. The Republican-controlled Texas Legislature drew new maps after the 2010 census was expected to yield at least three Republican victories in the four new U.S. House seats the state gained as a result of the Census.

But the state's population gain is largely a result of burgeoning numbers of Hispanics, who have strongly favored Democrats. Civil-rights groups challenged the Legislature's maps and, ahead of the state's March primary election, a federal court in San Antonio drew new districts to serve in the interim before a final decision was rendered. Texas is one of several states with a history of discriminatory voting practices required by the Voting Rights Act to obtain federal approval before altering electoral procedures or districts.

Arizona's illegal-immigration measure, officially titled the Support Our Law Enforcement and Safe Neighborhoods Act, reflected growing outrage among tea-party conservatives over what they considered lax enforcement by federal immigration authorities. Similar measures were introduced in other states, including Alabama, where officials were embarrassed after executives from German and Japanese car manufacturers the state fought to bring there were arrested for failing to produce immigration papers.

Those incidents and a backlash against the Arizona law have prompted second thoughts among some backers of state crackdowns. Last month, voters in Mesa, Ariz., recalled state Sen. Russell Pearce, the Republican firebrand behind SB 1070 and other measures targeting illegal immigrants. Mr. Pearce had begun the year on a high note after his colleagues elected him president of the state Senate, which he proclaimed would be the "tea-party Senate."

In May, over the objection of the Obama administration and the U.S. Chamber of Commerce, the Supreme Court upheld another Pearce measure that forced employers that repeatedly hired illegal immigrants to go out of business. The justices voted 5-4 along ideological lines to give expansive effect to a provision of federal law authorizing states to consider compliance with immigration rules when issuing business licenses. Mr. Pearce's law withdrew corporate charters and other required permits from such employers.

Although that opinion, by Chief Justice John Roberts, sympathized with states seeking to control the borders, it is unclear how the justices will read separate provisions of federal immigration law at issue in the SB 1070 case.

The court will have to reach its decision without the participation of Justice Elena Kagan, who recused herself from the case, apparently because she was solicitor general when the administration began formulating its legal challenge.