Adam Gowdiak, a researcher with Poland's Security Explorations who has discovered several bugs in the software over the past year, said that the update from Oracle leaves unfixed several critical security flaws.
"We don't dare to tell users that it's safe to enable Java again," said Gowdiak.
Some security consultants are advising businesses to remove Java from the browsers of all employees except for those who absolutely need to use the technology for critical business purposes.
HD Moore, chief security officer with Rapid7, a company that helps businesses identify critical security vulnerabilities in their networks, said it could take two years for Oracle to fix all the security bugs that have currently been identified in the version of Java that is used for surfing the Web.
"The safest thing to do at this point is just assume that Java is always going to be vulnerable. Folks don't really need Java on their desktop," Moore said.
An Oracle spokeswoman declined to comment.
Oracle said on its security blog on Sunday that its update fixed two vulnerabilities in the version of Java 7 for Web browsers.
It said that it also switched Java's security settings to "high" by default, making it more difficult for suspicious programs to run on a personal computer without the knowledge of the user.
Java is a computer language that enables programmers to write software utilizing just one set of code that will run on virtually any type of computer, including ones that use Microsoft's Windows, Apple's OS X and Linux, an operating system widely employed by corporations.
One version is installed in Internet browsers to access web content. Separate versions are installed directly on PCs, server computers and other devices including phones, webcams, and Blu-ray players.
The Department of Homeland Security and computer security experts said on Thursday that hackers figured out how to exploit the bug in a version of Java used with Internet browsers to install malicious software on PCs. That has enabled them to commit crimes from identity theft to making infected computers part of an ad-hoc networks that used to attack websites.
Oracle said that the flaws only affect Java 7, the program's most-recent version, and versions of Java software designed to run on browsers.
Java is so widely used that the software has become a prime target for hackers. Last year, Java surpassed Adobe Systems's Reader software as the most frequently attacked piece of software, according to security software maker Kaspersky Lab.
Java was responsible for 50 percent of all cyberattacks last year in which hackers broke into computers by exploiting software bugs, according to Kaspersky. That was followed by Adobe Reader, which was involved in 28 percent of all incidents. Microsoft Windows and Internet Explorer were involved in about 3 percent of incidents, according to the survey.
The Department of Homeland Security said attackers could trick targets into visiting malicious websites that would infect their PCs with software capable of exploiting the bug in Java.
It said an attacker could also infect a legitimate website by uploading malicious software that would infect machines of computer users who trust that site because they have previously visited it without experiencing any problems.
Security experts have been scrutinizing the safety of Java since a similar security scare in August, which prompted some of them to advise using the software only on an as-needed basis.
Meanwhile, Microsoft said on Sunday that would it release an update on Monday to fix a previously disclosed flaw in Internet Explorer versions 6, 7 and 8 that made PCs vulnerable to attacks in which hackers can gain remote control of the machines. Microsoft previously released a temporary fix to prevent such attacks.