ORLANDO, Florida (Reuters) - A Florida judge on Tuesday rejected a bid by George Zimmerman to delay his June trial for the murder of unarmed, black teenager Trayvon Martin, whom he shot and killed a year ago this month.

"I don't see any of your issues as insurmountable," Seminole County Circuit Court Judge Debra Nelson said in denying a motion by Zimmerman's lawyer, Mark O'Mara, for a continuance in the racially charged trial.

A memorial service for Martin, who would have turned 18 on Tuesday, was held on the courthouse lawn before the hearing got under way.

Before ruling, Nelson noted she had set aside several full days of court time for Zimmerman's defense attorneys and prosecutors to bring issues before the court, but most of that time had gone unused.

She also said O'Mara had been working on Zimmerman's defense since April 2012 and still has another four months to prepare for the June 10 trial.

O'Mara had told reporters he needed at least another six months to raise money and lay the groundwork for the trial. Zimmerman could face up to 25 years to life in prison if convicted of second-degree murder.

Prosecutor Bernie de la Rionda signaled his opposition to any delay in the trial last week and accused O'Mara of spending too much time conducting media interviews and not enough interviewing witnesses and examining evidence.

O'Mara testily told a news conference after Tuesday's hearing that it could be "physically impossible" for the defense to get fully prepared for the June trial date.

"We are busting butt on this case," he said, after Judge Nelson failed to cede any ground on the start date.

Jeopardizing his own ability to rely on expert witnesses at the trial, O'Mara told Nelson he would be unable to meet the judge's deadline for notifying prosecutors what experts he plans to call on to testify on Zimmerman's behalf.

Zimmerman, who is out on a $1 million bond, is living in hiding in central Florida pending his trial. At the time of the shooting, he was a neighborhood crime watch volunteer in a gated community where Martin was staying with his father.

The fair-skinned son of a white father and Hispanic mother, Zimmerman claims he shot Martin in self-defense following a confrontation that occurred as Martin was returning to the home of his father's girlfriend in the gated community after buying candy from a convenience store.

Police in the central Florida town of Sanford initially declined to arrest Zimmerman, citing Florida's "Stand Your Ground" law, which allows people to use deadly force when they believe they are in danger of getting killed or suffering great bodily harm.

The lack of an arrest led thousands to march in rallies in Florida and across the nation to demand justice for Martin. Protesters complained that African-Americans are seen as second-class citizens by the police and the U.S. justice system.

The fatal encounter between Martin and Zimmerman also threw the spotlight on gun control and Florida's much criticized "Stand Your Ground" statute, also known as a "shoot first" law, which was signed into law by former Governor Jeb Bush in 2005.

The law, backed by the National Rifle Association, was the first of its kind in the United States. Similar laws have been passed since in at least 23 other states, according to the Brady Campaign to Prevent Gun Violence.