It appears that the issue had been caused by custom admin's home page preset set up in the system:
mysql> select m.param, dbp.* from misc m, DashboardPreset dbp where dbp.id=m.val and m.param like '%preset%';
+------------------------+----+---------------------------------+-----------------------------------+----------+
| param | id | name | uri | type |
+------------------------+----+---------------------------------+-----------------------------------+----------+
| admin_custom_preset_id | 5 | 1-0 | /plesk/dashboard/ | custom |
| admin_preset_id | 11 | Default Administrator Home Page | /plesk/dashboard/ | admin |
| def_admin_preset_id | 11 | Default Administrator Home Page | /plesk/dashboard/ | admin |
| def_client_preset_id | 12 | Default Client Home Page | /plesk/client@/dashboard/ | client |
| def_domain_preset_id | 13 | Default Domain Owner Home Page | /plesk/client@/domain@/dashboard/ | domain |
| def_reseller_preset_id | 14 | Default Reseller Home Page | /plesk/reseller@/dashboard/ | reseller |
+------------------------+----+---------------------------------+-----------------------------------+----------+
6 rows in set (0.01 sec)
I have reviewed preset's configuration in table psa.DashboardPresetConfig but did not find any visible irregularities except the fact that it contains only 16 configuration parameters, while default administrator's preset consists of more than 117.If custom preset is disabled (by removing 'admin_custom_preset_id' parameter from psa.misc table) there are no errors reported and home page is displayed properly.
I have set up Parallels Plesk administrator to use default administrator's preset to allow Control Panel interface to work properly.