Under the plan, students struggling in English would be given exams in their native languages. A math test would be eliminated for some eighth graders. Students with disabilities would take tests matched to their level of instruction, not their age.

The proposals are modest, but they represent a rare concession from state leaders, who have faced attacks from parents and teachers in recent weeks over the rollout of a tougher set of standards known as the Common Core.

John B. King Jr., the state education commissioner, said that there was “more testing than is needed” in some districts and that some schools were too focused on rote memorization in preparing for exams.

“The amount of testing should be the minimum necessary to inform effective decision-making,” Dr. King wrote in a letter to superintendents and principals on Thursday.

Critics of high-stakes testing, however, said on Friday that the plan amounted to tweaks around the edges that would do little to change the culture of schools.

“It’s duplicitous,” said Monty Neill, executive director of FairTest, a group based in Massachusetts that opposes the use of high-stakes tests. “The political intention is to try to get students and parents to accept the bad system.”

Dr. King is also looking to eliminate some tests administered by local school districts. As part of the plan, the state would offer grants to districts to study the usefulness of exams and to eliminate redundancies.

The state would also seek to do away with a class of exams known as field tests, which are administered for the purpose of weeding out bad questions from future tests.

Elected officials and parents have denounced field tests in recent years, calling them unnecessary exercises that benefit testing companies and exhaust students. In New York City, a small number of families have protested field tests by boycotting the state exams.

In place of stand-alone field tests, the state would embed more field test questions into math and reading exams. That would require the Education Department to seek more money so it could print more versions of each exam. That could cost $12 million a year.

The department will pursue the changes over the next few months. In January, it will ask the federal government to allow English-language learners to take language arts exams in their native language; currently, students who have been in the United States for at least a year must take those exams in English.

The state will also seek permission for some 57,000 eighth-graders studying algebra to take a Regents exam in lieu of a traditional math test. Those students are currently required to take both.

Responding to an outcry over lax standards, the state has taken several steps since 2009 to improve the quality of exams, including developing new tests in reading and math that are aligned with the more rigorous Common Core curriculum. Student passing rates fell sharply when the new exams made their debut last school year, a demoralizing blow for many educators.

Leaders of teachers’ unions and parents have become increasingly vocal in their criticism of the state’s efforts. In recent weeks, some parental leaders have called for Dr. King to resign, saying that the state is rushing to adopt the Common Core and that it should not use results from the new exams to evaluate schools, teachers and students.

In New York City, where concerns over testing have seeped into the mayoral race, there was criticism of the state’s plan.

“All this emphasis is being put on testing, instead of developing an enriched curriculum that produces real learning for children,” said Jane Hirschmann, co-chairwoman of Time Out From Testing, a statewide coalition. “This is not going to satisfy any of us.”

The city’s Education Department, however, praised Dr. King’s efforts.

“It’s a thoughtful response to schools’ concerns on this issue,” Erin Hughes, a spokeswoman for the department, wrote in an e-mail. “We welcome the additional flexibility.”