Wikipedia puts Macau in second place, using data as of July 2005 and taken from the United Nations World Populations Prospects Report (2004 revision).
Monaco........ 23,660 people per sq km
Macau......... 17,699 people per sq km
Hong Kong...... 6,407 people per sq km
Singapore...... 6,333 people per sq km
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The Singapore government gives these figures:
Population Density (Per Sq Km) (for year 2005) 6,222
The
People's Daily Online (China) has this to say, on August 25, 2005:
Macao recorded the world highest population density of 17,309 per square kilometer on June 30, according to official statistics issued here on Thursday.
The figures from the Statistics and Census Service showed that the region's resident population reached 476,000 on the date, a year-on-year increase of 4.1 percent.
The special administrative region's population has risen 46,400,or 10.8 percent, since 1999 when it returned to the motherland, according to the statistics.
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It appears that the answer may depend on the source, and one's definition of exactly what constitutes a country.