HOUSTON — A judge dismissed Tuesday the last of the charges against two anti-abortion activists who covertly recorded a video of themselves meeting with Planned Parenthood officials, effectively ending a case that had drawn national attention from both opponents and supporters of abortion rights.

The activists, David R. Daleiden, 27, and Sandra S. Merritt, 63, were indicted in January by a grand jury here in Harris County on charges of tampering with government records for using fake identification and offering to buy fetal tissue at a meeting at which Planned Parenthood officials explained how they provided the tissue to medical researchers. Their video, one of several widely circulated on the internet, said Planned Parenthood was guilty of selling fetal remains, accusations Planned Parenthood has denied.

After the videos surfaced last year, Dan Patrick, the Texas lieutenant governor, a Republican, asked the Republican district attorney in Harris County to open a criminal investigation into Planned Parenthood in August. A grand jury ended up indicting Mr. Daleiden and Ms. Merritt, and taking no action against Planned Parenthood.

At a hearing in the case on Tuesday, prosecutors with the Harris County district attorney’s office asked the judge to dismiss the charges, citing a potential legal issue with the grand jury’s term, which had been extended during the investigation. Mr. Daleiden’s lawyers had argued that the grand jury did not have the authority to indict Mr. Daleiden and Ms. Merritt during the extension, and prosecutors appeared to have agreed.