AMSTERDAM (Reuters) - Libya said on Tuesday it will complete its investigation of Muammar Gaddafi's son, Saif al-Islam Gaddafi, within weeks for crimes including murder and torture, and asked the International Criminal Court once again to hold off ordering his surrender.

Libya's government and the war crimes court - which indicted Saif al-Islam in June for crimes against humanity stemming from the crackdown on last year's revolt - have argued for months over where he should be tried.

Tripoli considers it a matter of national pride and a measure of the country's transformation for Saif al-Islam's trial to be held in Libya. Human rights groups question whether its justice system can meet the standards of international law and say he should be handed over to the ICC instead.

The Libyan government has again challenged the admissibility before the ICC of the cases concerning both Said al-Islam and Abdul al-Senussi, Gaddafi intelligence chief, according to a document released by The Hague-based court on Tuesday, saying its own investigations "are now at an advanced stage."

"They are expected to be completed in the near future," Libya's government said in the document.

"It is anticipated that the investigative phase of proceedings with respect to Mr Gaddafi will be completed within the next few weeks," it added, whereas for al-Senussi, the proceedings will take longer because he is not in the country and suffers from a liver disease.

Al-Senussi was arrested in Mauritania in March and is wanted by Libya, France and the ICC.

"Mr Al-Senussi's liver disease has become apparent and his health condition is now such that it is understood that he cannot presently be investigated domestically for breaches of Mauritanian law, let alone transferred back to Libya," Libya said in the court document.

"The justice ministries of both countries are in regular contact and are monitoring Mr Al-Senussi's condition in order to determine when his transfer will be possible," it added.

Libya also refuted allegations that Said al-Islam had been physically attacked and misled over the charges against him, saying he had been provided with proper medical and dental care and had not been physically abused.

"Mr Gaddafi has been kept in adequate conditions of detention (which will be improved even further upon his transfer to newly constructed prison facilities in Tripoli), provided with sufficient and good quality food (the same food as that consumed by his prison guards)," it said in the document.

(Reporting by Sara Webb; Editing by Michael Roddy)