From the link posted:
-----Are all Jews around the world descended from the Khazars? Certainly not.-----
The Ashkenazi Jews are also the direct descendants of the Israelites. Genetic tests seem to indicate that Jewish ancestry largely comes from the regions known today as Turkey, Armenia, Israel, and Iraq. Mediterranean Fever, for example, is found among some Ashkenazi Jews as well as Armenians and Anatolian Turks. Many Ashkenazi men who belong to the priestly caste (Kohenim) possess the "Cohan modal haplotype" (CMH) on the Y-chromosome. While not exclusive to Jews, the CMH is found mostly in peoples from the north-eastern Mediterranean region (and, incidentally, among Palestinian Arabs), and its distribution supports the claim that Jews who have the CMH have an ancestral line from the Middle East. A genetics study released in May 2000, led by Michael Hammer, contends that the results show that Ashkenazi Jews are more closely related to Yemenite Jews, Iraqi Jews, Sephardic Jews, Kurdish Jews, and Arabs than they are to European Christian populations, and that hardly any intermarriage or conversion has occurred to affect the Jewish groups over the centuries. A study the following year by Ariella Oppenheim et al. showed why it is important to include multitudes of comparisons between ethnic groups; Hammer had failed to test Kurds and any Slavic group other than Russians, whereas Oppenheim's team did so and therefore came to somewhat different conclusions. But, in general, evidence from both studies is strong that most Ashkenazic Jews descend from Judeans in their paternal lineages. DFNB1, a genetic mutation causing deafness, affects Jews as well as Palestinians and other Mediterranean populations, according to research by Dr. Aravinda Chakravarti. A particular mutation that causes coagulation factor XI deficiency is found among both Iraqi Jews and Ashkenazi Jews, from a common ancient ancestor over 2000 years ago. Discussions and summaries of genetic evidence are here.

The population geneticist Nathaniel Michael Pearson worked with the Human Genome Project a few years ago and helped to collect DNA samples from North Caucasians, Turks, Sino-Tibetans, and other groups. Pearson is of Ukrainian Jewish background and compared his paternal Y-chromosome sample to those of men from other groups. His DNA matched with an Uzbekistani Uzbek, an Uzbekistani Tajik, and two men from New Delhi in northern India. Pearson believes that the Central Asian haplotype he has could be connected to the Khazar Turks. However, he told me that this haplotype "appears at only a couple percent frequency in a large Ashkenazi sample (and strangely shows a slightly higher, but still very low, frequency among Moroccan Jews)". In other words, this particular possibly-Khazar ancestral strain represents a minority rather than a majority of Eastern European Jews. And while maternal DNA (mtDNA) studies have shown substantial links between Ashkenazi Jews and the peoples of Europe, these non-Israelite inputs into the Ashkenazi genepool still do not represent the majority of total maternal and paternal Ashkenazi ancestry, and probably only some of these European inputs come from Khazar women.

Additional, more comprehensive genetic testing may help us to understand the extent of any Khazar contribution to the Ashkenazi gene pool. For now, I can point out that the Israelite traces among the East European Jews came from three sources: (1) Sephardic Jews fleeing Spain and Portugal and resettling in Lithuania and Poland, (2) Roman Jews, and from (3) Khazarian Jews who merged with Israelites, just as the Schechter Letter states "they became one people". The Khazars and the Israelites mixed with each other.

Are all Jews around the world descended from the Khazars? Certainly not. East European Jewish ancestry originates substantially from ancient Judea, and the same is true of most other modern Jewish populations (with the exception of groups like Libyan Jews and Ethiopian Jews). But, it is rational to conclude that some Jews also have some Khazar ancestors.