The petition had more than 500 signatures by Friday afternoon. It said the district should "not force redistricting on any family."
The petition to the school board reflects comments made Thursday at a public redistricting forum at Lafayette High School.
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Earlier this year, the school board adopted goals for a redistricting plan that will be proposed to the board in early 2015.
No one goal is weighted more heavily than others, Superintendent Tom Shelton said Friday.
But socioeconomic balance — having a mixture of students from varying social classes — "is a primary consideration identified by the school board because it is directly tied to student achievement," Shelton said.
"Education research demonstrates that all students achieve better in diverse settings — including those from high income families, middle income families and low income families," he said.
"We understand and respect that every person who has signed the petition wants what is best for kids, as do we."
In Fayette County, some elementary schools have less than 15 percent of students who are eligible for free or reduced-price lunch. Others have well over 90 percent.
Parents said having children go to the school closest to their home, not socioeconomic balance, should be the main goal.
Shelton said the school board "also recognizes the desire of some families to attend schools close to their homes, and has identified proximity as another desirable outcome."
The website did not indicate who is behind the group called Fayette County Citizens that posted the petition on June 6.
But the web page explaining the petition said, in part, "Although balancing socio-economic status in schools has been stated as a primary consideration in drawing school boundaries, it is widely documented that letting students go to the local school in their community, even if it means that most of the students would be the same race or socioeconomic status, is greatly preferred by a majority in the community."
Redistricting all of Lexington's public-school boundaries is being necessitated by a new high school on Winchester Road and two new elementary schools, one on Georgetown Road and another east of Interstate 75.
Officials said the elementary schools should open in fall 2016; the high school should open in fall 2017.
The petition said the Fayette County School Board should reach a resolution that improves academic achievement for all students. The resolution should be one that delivers "the resources necessary to improve the learning environment in schools with students of relatively lower socioeconomic status," the petition said.
Shelton said the school board also placed "the achievement of all students as the foundation for every decision related to new attendance boundaries."
The petition said district officials should "pursue as its primary consideration the principle of attending a school close to your home and with those that live in the same neighborhood rather than socioeconomic status."
At least 90 signatures were anonymous.
One woman who signed her name to the petition, Carrie Rudzik, said she had no problem with socio-economic balance being one factor, but she thought neighborhood schools should be the primary goal.
Rudzik said in an interview that she signed the petition because she lives across the street from Glendover Elementary and she does not want her children to be reassigned to another school.
"My husband and I just purchased a home with the primary factor being the school district," Rudzik said in comments attached to the online petition. "I'm sure there are many other families who have done the same."
Parent Lindsey Ingram, who spoke at Thursday's public forum, said he also signed the petition.
"We are very concerned about this process and how it's going to play out," he said.
Ingram said he thought that parents at all socio-economic levels want their children to finish at the elementary school where they started and attend a school that's close to where they live.
Meanwhile, school board member Amanda Ferguson said she wanted to make it clear to citizens that when the school board approved the goals, they were in no particular order of priority.
The committee that is developing a redistricting plan includes school board members, business leaders, Equity Council members, parents, Realtors, home builders, principals and city planning officials.
The last time redistricting was undertaken on a large scale was in 2002.
At this point, the redistricting committee is early in its work, Shelton said, and has not begun discussing any specific proposals.
Committee members "will grapple with how to achieve the very best solution for our entire community, using student achievement as the arbiter in decisions," Shelton said.