According to the AFP newswire, Islamist radicals are suspected of being behind the DDOS attacks, which apparently downed the newspaper site for around 10 hours last Tuesday.
Editor Berat Buzhala is quoted by the newswire as saying his paper's site had previously been targeted for coverage of religious issues.
Kosovo's majority Albanians, he explained, are mostly Muslim, although the country is largely secular.
"This latest attack has gotten us worried a bit," he said, adding that the newspaper and it readers need to know who the DDOS attackers are.
Via the newspaper, Buzhala is urging Kosovan leaders to denounce the hacking attacks against the website.
Newswire reports suggest that the site was attacked by hackers because it was covering the trial of a Kosovar charged in the US with plotting terrorist acts.
As well as being effective downed with a DDOS attack, hackers reportedly left a warning on the newspaper site to the "anti-Islamic newspaper to stop ridiculing" Muslims.
Infosecurity notes that the Albanian-language Express newspaper has been covering the trial of Hysen Sherifi, aged 24, an ethnic Albanian from Kosovo.
Sherifi and six American citizens were arrested late last month on suspicion of conducting military-style training in preparation for `violent jihad' in Jordan, Pakistan, Israel and Kosovo.
Although Kosovo has a population of more than two million people and has its own telephony country code, it does not have its own top level country domain, nor are its internet resources sophisticated.
Despite this, internet cafes can be found in most towns and cities, with many cafes using VSAT BGAN satellite links into the global internet for high-speed stable connections.
In theory, the limited internet access in the country should help prevent a DDOS attack on a major site, but, for logistical reasons, many websites are hosted outside of the country, so making a DDOS attack feasible using botnets also operating international, Infosecurity notes.